Question

Rationalinzing Expressions: x^2 +2x over 12x +54 - 3-x over 8x +36

Answer 1

x^2 + 2x =

x(x+2) 1
_______________ x ____________________

11x + 51 4(2x + 9)

Then simplify

Answer 2

is the problem

\[\frac{ x^2 + 12x}{12x - 54} - \frac{3 - x}{8x + 36}\]

Answer 3

yes @campbell_st

Answer 4

Just kidding I meant x^2 + 2x

Answer 5

it should look like \[x^2 + 2x \over 12x + 54 \]

Answer 6

thank you.... then with some factorizing you get

\[\frac{x(x+12)}{6(2x - 9)} - \frac{3 - x}{4(2x + 9)}\]

multiply the denoninators to get a common denominator and cross multiply the numerators

\[\frac{x \times(x+12) \times 4\times(2x+9) - (3 - x) \times 6\times(2x-9)}{6(2x-9)\times 4(2x +9)}\]

you'll need to expand and collect like terms... the denominator is the difference of 2 squares.

\[\frac{4x \times (2x^2 + 33x + 81) - 6\times (-2x^2 +15x - 27)}{24\times(4x^2 - 81)}\]

simplify and collect like terms

\[\frac{ 8x^3 + 144x^2 +234x + 162}{24\times(4x^2 - 81)}\]

\[\frac{4x^3 + 72x^2 + 117x + 81}{12(4x^2 - 81)}\]

Answer 7

@campbell_st , the original number was 2 not 12. It would completley change the equation wouldnt it?

Answer 8

yes it would